Bounded Functions in Möbius Invariant Dirichlet Spaces

Forp∈(0, 1), letQ_p(Q_{p, 0}) be the space of analytic functionsfon the unit diskΔwith sup_w∈Δ ‖f°?_w‖_p<∞ (lim_|w|→1 ‖f°?_w‖_p=0), where ‖·‖_pmeans the weighted Dirichlet norm and?_wis the Möbius map ofΔonto itself with?_w(0)=w. In this paper, we prove the Corona theorem for the algebraQ_p∩H^∞(Q_{p, 0}∩H^∞); then we provide a Fefferman–Stein type decomposition forQ_p(Q_{p, 0}), and finally we describe the interpolating sequences forQ_p∩H^∞(Q_{p, 0}∩H^∞)).     

Spectra of regular polytopes

In this paper we compute the spectra with multiplicities of the adjancency graphs of all regular polytopes in ⁿ : it turns out that all such eigenvalues are algebraic intergers of degree no greater than 3.Both authors receive continuous support from FINEP and CNPq, Brazil.     

On deformations of transversely homogeneous foliations

A transversely homogeneous foliation is a foliation whose transverse model is a homogeneous space G/H. In this paper we consider the class of transversely homogeneous foliations on a manifold M which can be defined by a family of 1-forms on M fulfilling the Maurer–Cartan equation of the Lie group G. This class includes as particular cases Lie foliations and certain homogeneous spaces foliated by points. We develop, for the foliations belonging to this class, a deformation theory for which both the foliation and the model homogeneous space G/H are allowed to change. As the main result we show that, under some cohomological assumptions, there exist a versal space of deformations of finite dimension for the foliations of the class and when the manifold M is compact. Some concrete examples are discussed.     

A reliable analytical approach based on gas chromatography coupled to triple quadrupole and time‐of‐flight mass analyzers for the determination and confirmation of polycyclic aromatic hydrocarbons in complex matrices from aquaculture activities

The potential of gas chromatography coupled to tandem mass spectrometry (GC/MS/MS) with a triple quadrupole analyzer (QqQ) has been investigated for the quantification and reliable identification of sixteen polycyclic aromatic hydrocarbons (PAHs) from the EPA priority list in animal and vegetable samples from aquaculture activities, whose fat content ranged from 5 to 100%. Matrices analyzed included fish fillet, fish feed, fish oil and linseed oil. Combining optimized saponification and solid‐phase extraction led to high efficiency in the elimination of interfering compounds, mainly fat, from the extracts. The developed procedure minimized the presence of these interfering compounds in the extracts and provided satisfactory recoveries of PAHs. The excellent sensitivity and selectivity of GC/(QqQ)MS/MS in selected reaction monitoring (SRM) allowed to reach limits of detection at pg/g levels. Two SRM transitions were acquired for each analyte to ensure reliable identification of compounds detected in samples. Confirmation of positive findings was performed by GC coupled to high‐resolution time‐of‐flight mass spectrometry (GC/TOFMS). The accurate mass information provided by GC/TOFMS in full acquisition mode together with its high mass resolution makes it a powerful analytical tool for the unequivocal confirmation of PAHs in the matrices tested. The method developed was applied to the analysis of real‐world samples of each matrix studied with the result of detecting and confirming the majority of analytes at the µg/kg level by both QqQ and TOF mass spectrometers. Copyright © 2009 John Wiley & Sons, Ltd.     

An atlas for tridiagonal isospectral manifolds

Let be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix Λ with simple spectrum. We introduce bidiagonal coordinates, charts defined on open dense domains forming an explicit atlas for . In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, every matrix in now lies in the interior of some chart domain. We provide examples of the convenience of these new coordinates for the study of asymptotics of isospectral dynamics, both for continuous and discrete time.     

High beam quality in a HyBrID copper laser operating with an unstable resonator made of a concave mirror and a plano-convex BK7 lens

This paper presents a very simple unstable resonator, made of a concave mirror (total reflector) and a bare plane–convex BK7 lens working as a convex coupling mirror, which is quite efficient for HyBrID copper laser. In addition to a good quality factor (M²=4.9), experimental results showed that it is possible to control the laser output power by introducing a variable aperture iris inside the cavity, close to the coupling lens, without spoiling beam quality. A rough theoretical model helped to explain these results as a combined effect of unstable resonator plus radial gain distribution.     

Electrical impedance spectroscopy of epoxy systems II: Molar fraction variation, resistivity, capacitance and relaxation processes of 1,4-butanediol diglycidyl ether/succinic anhydride and triethylamine as initiator

The Electric Impedance Spectroscopy (EIS) was used to evaluate resistivity, capacitance and relaxation processes of a cured epoxy system with different molar composition of 1,4-butanediol diglycidyl ether (EP), succinic anhydride (SA) and triethylamine (TEA) as initiator. The measurements were done over range frequencies between 10⁻¹ and 10⁵ Hz. The systematic change of the molar fraction composition affected the resistivity and capacitance changes indicating gelation critical compositions according to the Flory’s aggregation theory. The complex electric functions, dielectric constant ε^•, electric modulus M^•, impedance Z^•, admittance Y^• and the loss factor tan δ were utilized in order to investigate the relaxation processes. Relaxation peaks were observed for different molar fraction composition only in the imaginary impedance, the electric modulus and the tan δ as frequency functions. The relaxation frequencies obtained by Z″, M″ and tan δ evaluation are distinct and have been discussed in terms of resin components molar fraction dependence.     

Quantitative immunofluorescent assay of full-length,recombinant CD4 in solution and mapping of its epitopes

A specific, rapid, and sensitive method for the detection of CD4 in solution was developed using pairs of fluorescently stained monoclonal antibodies which do not cross-compete. The assay is quantitated by flow cytometry using Simply Cellular microbeads (SC beads) as the primary support for the first anti-CD4 mAb. This method uses the standard conditions for anti-CD4 monoclonal antibody binding, washing, detection, and quantitation by flow cytometry of the CD4 antigen either bound to the SC beads or expressed on the cell surface. The monoclonal antibody used (Leu 3a PE) is the standard reference used to evaluate the CD4 concentration. This method differs from ELISA techniques, which need an antigen standard curve and thus can be influenced by the quality and source of the antigen. This type of assay is also a procedure which enables determination of the level of oligomerization of the bound antigen. It can be used for any antigen to which monoclonal antibodies recognizing at least two distinct epitopes are available. The use of soluble or full-length CD4 derivatives as potential therapeutic agents against AIDS, would benefit from a precise quantitation of the CD4 molecules which still have their proper tertiary structure.